What ailment might the narrator suffer? How does the narrator use personification throughout the story?

It seems that the narrator is suffering from what we would call postpartum depression, though they did not have such a diagnosis when Gilman wrote the story. The narrator's husband, a doctor, tells friends and family that she has only a "temporary nervous depression—a slight hysterical tendency." A diagnosis of hysteria tended to function as a sort of catchall for any mental problems that seemed particularly associated with women: in fact, the word hysteria comes from the Greek word for uterus. Further, the narrator talks about how glad she is that "Mary is so good with the baby. Such a dear baby! And yet I cannot be with him, it makes me so nervous." Her confession that being with her baby makes her feel nervous is a good indicator that the state of her mental health has a great deal to do with the fact that she's recently given birth and that she is not, perhaps, connecting with her child in the way that one might hope or expect.
Throughout the story, the narrator routinely personifies the wallpaper in her room. For example, she says,

There is a recurrent spot where the pattern lolls like a broken neck and two bulbous eyes stare at you upside down [....]. Up and down and sideways they crawl, and those absurd, unblinking eyes are everywhere [....]. I never saw so much expression in an inanimate thing before, and we all know how much expression they have! I used to lie awake as a child and get more entertainment and terror out of blank walls and plain furniture than most children could find in a toy-store. I remember what a kindly wink the knobs of our big, old bureau used to have, and there was one chair that always seemed like a strong friend.

She gives the design of the wallpaper a neck and eyes and the ability to crawl. Not only does she attribute life to the wallpaper itself, but it also seems to have been a pattern with her, throughout her life, to personify all kinds of objects. She talks about how inanimate things always seem to have a great deal of expression to her: a pretty atypical description of things like walls and wardrobes. This helps gives us some insight into her imagination as well; she is clearly very creative and thoughtful and that must make it all the more frustrating and upsetting for her that her husband has removed all means of mental stimulation from her room.